# TENSILE STRESS IN A BAR

Tensile Stress in a Bar Calculator has been developed to calculate tensile stress (or compressive stress), normal/shear stress on any oblique section of the bar, longitudinal/lateral strain, longitudinal/lateral deflection and total strain energy. The deformed bar under tensile stress is shown in the following figure.

If a straight bar, of any cross section, of homogeneous material, is axially loaded , the bar elongates under tension and shortens under compression. On any right section to the load, there is a uniform tensile (or compressive) stress. On any oblique section, there is a uniform tensile (or compressive) normal stress and a uniform shear stress.

Basic assumptions for "Tensile Stress in a Bar Calculator" are:

- The loads are applied at the center of ends,

- Uniform stress distribution is occured at any section of the bar,

- The bar is constrained against buckling,

- The stress does not exceed the proportional limit.

##### Calculator:

 INPUT PARAMETERS Parameter Symbol Value Unit Applied Load P N kN lbf Cross-sectional Area (before loading) A mm^2 cm^2 inch^2 ft^2 Length (before loading) l mm cm m inch ft Lateral Dimension d Elastic Modulus E GPa ksi Poisson's Ratio ν --- Angle θ deg

 OUTPUT PARAMETERS Parameter Symbol Value Unit Tensile Stress σ --- MPa psi ksi Normal Stress in any Oblique Plane σθ --- Shear Stress in any Oblique Plane τθ --- Longitudinal Strain ε --- --- Lateral Strain ε' --- Longitudinal Deflection δ --- --- Lateral Deflection δ' --- Total Strain Enegy U --- J ft-lb in-lb

##### Supplements:

 Link Usage Material Properties Thermal expansion coefficient and elastic modulus values of steels, aluminum alloys, cast irons, coppers and titaniums.

##### List of Equations:

 Parameter/Condition Symbol Equation Tensile Stress σ σT = P/A Normal Stress in any Oblique Section σθ σθ = (P/A)*cos2θ Shear Stress in any Oblique Section τθ τθ = (P/2A)*sin2θ Longitudinal Strain ε ε = σ/E Longitudinal Deflection δ δ = (Pl)/(AE) Lateral Strain ε' ε' = -νε Lateral Deflection δ' δ' = ε'd